Suppose we run a regular multiple regression of a response variable y on 3 predictors, and find the following output. Estimate Std. Error t value Pr(>|t|) (Intercept) -0.7620 0.5268 -1.446 0.155 х1 x2 -5.3746 4.1160 -1.306 0.198 2.9286 2.5733 1.138 0.261 x3 2.9031 1.3875 2.092 0.042 * Signif. codes: 0**** 0.001 *** 0.01 ** 0.05 ' 0.1 '' 1 Residual standard error: 1.121 on 46 degrees of freedom Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692 F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597 Suppose instead we decided to centre the response and predictors (centred at their mean, e.g. (y – y), (x1 – x1), etc.), and run the regression on these centred values. What would the value of the intercept be?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Suppose we run a regular multiple regression of a response variable y on 3
predictors, and find the following output.
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.7620 0.5268 -1.446 0.155
х1
-5.3746 4.1160 -1.306 0.198
x2
2.9286 2.5733 1.138 0.261
x3
2.9031 1.3875 2.092 0.042*
Signif. codes: 0**** 0.001 ** 0.01 ** 0.05 ' 0.1 '' 1
Residual standard error: 1.121 on 46 degrees of freedom
Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692
F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597
Suppose instead we decided to centre the response and predictors (centred at their
mean, e.g. (y – ỹ), (x1 – x1), etc.), and run the regression on these centred values.
What would the value of the intercept be?
Transcribed Image Text:Suppose we run a regular multiple regression of a response variable y on 3 predictors, and find the following output. Estimate Std. Error t value Pr(>|t|) (Intercept) -0.7620 0.5268 -1.446 0.155 х1 -5.3746 4.1160 -1.306 0.198 x2 2.9286 2.5733 1.138 0.261 x3 2.9031 1.3875 2.092 0.042* Signif. codes: 0**** 0.001 ** 0.01 ** 0.05 ' 0.1 '' 1 Residual standard error: 1.121 on 46 degrees of freedom Multiple R-squared: 0.1053, Adjusted R-squared: 0.04692 F-statistic: 1.804 on 3 and 46 DF, p-value: 0.1597 Suppose instead we decided to centre the response and predictors (centred at their mean, e.g. (y – ỹ), (x1 – x1), etc.), and run the regression on these centred values. What would the value of the intercept be?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman